Відео

Im pretty new to calculus and i have a question if anyone would care to help me. I know how to find the derivative of sqrt(x) by using the power rule. f'(x)=1/2sqrt(x) But how do i find it using the limit definition? Is the following correct.... Lim h->0 f(x)=sqrt(x) Lim h->0 f(x+h)-f(x)/h Lim h->0 f(sqrt(x+h))-f(sqrt(x))/h Is that correct? Am i to assume that both x and h are roots? Or would it be better to look at it like this... lim h->0 f(x+h)^1/2-f(x)^1/2 --------------------------- h

Just wanted to say that you are my hero and actually i Ve learned a lot from you 😊

Thank You * d/dx [1Billion*x] times 😅

Always interesting.

Your channel is my go-to for lifting my spirits. Thank you for being a constant source of joy.

🤩👍

Your'e also teaching us how to make videos by setting them up for editing but not actually editing!

Analysis and calculus IS it thé same ??

Was needing to catch up on some specialist mathematics (Calculus 2 I guess) and I had no idea how to rationalise the 3rd/4th example using that form of partial fraction. This demonstration was so clear and now I have a simple way to rationalise and complete these problems, thanks so much!

I feel that the calc3 videos are in the wrong order somehow. For example, the Unit Tangent Vector has been mentioned i several videos already, but isn't explained until now. But the explanation is excellent, as per usual.

Loving this new series, please keep it up

Thank you sir

A very good and clear to follow video but also can we give credit to how flawlessly and quickly the switch between black and red marker is! I’m very impressed!

Very, very nice presentation. So, ( apologies if I am spoiling your next video ) .....where, exactly, is vector N pointing?? - toward a very special point. Your current and recent videoes have already given us the answer. It is staring right at us.

Differential Geometry is the coolest! Well, coolest except for Clifford Algebra and Geometric Calculus :-)

Appreciate your help! Truly grateful!

Dang why did this one fail so badly? The algorithm did you dirty

What if we use l'Hôpital's Rule? Like by rearranging the original equation so that if I put 1 in the f(x) I would either get 0/0 or ∞/∞.

This dude looks like he could he either 25 or 41

Calculus 3 videos are very interesting! Can't wait for the next one

Super cool that you’re doing calc III videos now. Very interesting and well explained as always 💯

Deetee deeree! T! Deetee? Plus N! TNT. Boom!

Nice video. But please stop saying divide by dt (as in 1:53). It is not how derivative works.

I LOVE YOU

Thanks, and is the converse true?

found another nice proof using e can find such a number 𝐶 C if we restrict 𝑥 x to lie in some interval centered at 2. For example we can take: ∣ 𝑥 − 2 ∣ < 1 ∣x−2∣<1 − 1 < 𝑥 − 2 < 1 −1<x−2<1 − 1 + 2 < 𝑥 − 2 + 2 < 1 + 2 −1+2<x−2+2<1+2 1 < 𝑥 < 3 1<x<3 Step 6 6 of 11 The function 𝑦 = 𝑥 2 + 2 𝑥 + 4 = ( 𝑥 + 1 ) 2 + 3 y=x 2 +2x+4=(x+1) 2 +3 is increasing for 𝑥 ∈ ( − 1 , ∞ ) x∈(−1,∞). Thus we have: ∣ 𝑥 2 + 2 𝑥 + 4 ∣ = ∣ ( 𝑥 + 1 ) 2 + 3 ∣ < ( 3 + 1 ) 2 + 3 = 19 , for 1 ≤ 𝑥 ≤ 3. ∣x 2 +2x+4∣=∣(x+1) 2 +3∣<(3+1) 2 +3=19,for 1≤x≤3.

I don't know why, this has never happened to me before I don't think, but the example given felt absolutely worthless. The example itself was completely fine, but we just proved that if a vector has constant magnitude then its derivative is orthogonal to it. Then we picked a vector with a constant magnitude. Then we calculated the dot product to verify that it is indeed 0, as expected, but it obviously would turn out to be 0, we JUST proved that it would be given the property that it has, and the proof had no mistakes or assumptions or anything, so why would you need to verify? Don't get my words twisted, this is THE FIRST TIME I think about a proof+example in this way, it has nothing to do with this specific one, it was great, but I just wanted to yap unnecessarily.

very talented took me many hours and 3 watching but starting to get it

I absolutely love how you explain and the examples that you put! You’re making me feel like I will be able to integrate one day 😂🤣❤️❤️🤞🤞🤞

We did have a similar exercise in with we needed to find the smallest line form a point on a e Funktion and its solution of the tangensequtaion

Why does such a smart man feel he needs to hold a mic that clips on to your clothing?

good post this morning!

5:43 Not the Best Friend, but a good friend.

Wow! But why this important 🙏🏻🤔

Your video helped me gain a new skill. I feel more confident thanks to your tutorials.

I think the proof can be easier when you know the vector is on a sphere or circle in R2. You just need to proof r'(t) is tangent to r(t), which is powerful beginner equation for Multical

1/3 sin (1) Is thé Area of which part ??

I am from India and I am currently studying in high school...I will request you to please upload a vedio on polar coordinate system.... including the basic topics like del operator in polar coordinate system...because It is very hard for me to understand these topics......and these are very important to find Force of Attraction between dipole in physics.....❤❤

If someone need proof that it go past 3 , I dont know, maybe go to school again..

Thta whole class is full of dumb or actually the teacher may not be appropriate as this is most basic limit i have ever seen, in India a 6 six class fellow that can do that without using pen.

I never liked that term "approaches" infinity. Too vague, and without refinement. Approaches infinity means on the path to it, or not. Only exactly one.

When I begin calculus, I am certain I will be watching a lot of your videos. Good content!

very rigorous proof

how is this calculus? This is just a wedge minus a wedge. This is super basic geometry.

I might be wrong but I think when you were taking the derivative of the function k you did the derivatives of e to the powers wrong where they should be -2/3e^(-5/3) and 4/3e^(1/3) so you brought the powers down correctly for the power rule just didn't subtract 1 from the exponent.

Does it matter which is the parametrization or is it like the line integral?

Thanks

Why? substitute s=x-1 immediately yields x/(x-1) = s/s+1/s as s->0+ positive inf, s->0- negative inf. Therefore undefined